In TNT stereochemical restraints are simply listed. The order is unimportant and the completeness is unimportant. You can define bond lengths, bond angles, torsion angles, (pseudorotation angles,) planes, and chiral centers.
The REFI format contains two types of information. One is a set of pointers which define, in a rigorous fashion, the connectivity of the molecule. The other is a set of bond lengths, angles, and torsion angles.
The first difference you will notice is that TNT does not explicitly define the connectivity of the molecule. The format conversion routine builds such a table from the bond length, bond angle, torsion angle, and chiral center definitions. However, even TNT requires that all bond lengths be defined (otherwise the bonded atoms will be pushed apart because of a ``bad" contact). You should never experience a problem because of an undefined bond length.
While REFI does not require that every bond angle be defined it is quite insistent that the bond angles it wants are defined. You will not be able to predict which angles are required. Convert will produce an warning message for each missing angle. You can add these angles to you TNT geometry definition file and run Convert again.
REFI has two different functions and these two functions make differing uses of the torsion angles. The usual mode of REFI is to regularize a model. When regularizing REFI only uses the torsion angle values for particular angles which have been marked as ``fixed". If you have forgotten to define an torsion angle, or the angle has been defined with multiple correct values Convert will mark the angle as ``variable". You will still be able to regularize your molecule but these torsion angles will not be idealized. This is only a problem for planes.
REFI uses torsion angle restraints to enforce planarity. If you have not defined the torsion angles of the planar group to be single valued, as either cis or trans, REFI will not produce a group which is flat. You will receive warning messages about each ambiguous torsion angle. You are not required to do anything about these warnings but you will get better results if you have fewer warnings.
The REFI format uses a ``tree" data structure to represent the connectivity of the molecule and every tree must have a root. TNT is fairly arbitrary about its choice of root. If its choice is not satisfactory you can change it by reordering the GEOMETRY statements. Place the statements which define the bond for your root first and TNT will chose it as the root. I know of no reason to worry about the particular atom at the root so you should never have a problem with this.